Question

How do you find the exact functional value sin(405°+120°) using the cosine sum or difference identity?

Answer 1

Find: sin (405 + 120)

Ans: `(sqrt6 - sqrt2)/4`

Explanation:

sin (405 + 120) = sin (45 + 120) --> because 405 = 45 + 360 deg
Apply the trig identity: sin (a + b) = sin a.cos b + sin b.cos a
`sin 45 = sqrt2/2` ; and `cos 120 = -1/2`
`sin 120 = sqrt3/2` ; and `cos 45 = sqrt2/2`

`sin (45 + 120) = (sqrt2/2)(-1/2) + (sqrt3/2)(sqrt2/2) =`
`= (sqrt6 - sqrt2)/4`

Check by calculator: sin (45 + 120) = sin 165 = 0.26
`(sqrt6 - sqrt2)/4` = 0.26 OK